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• Vl-consteval

Vl-consteval-unary-reduxop

Signature

(vl-consteval-unary-reduxop op aval width) → ans

Arguments

op — Guard (member op '(:vl-unary-bitand :vl-unary-nand :vl-unary-bitor :vl-unary-nor :vl-unary-xor :vl-unary-xnor :vl-unary-lognot)) .

aval — Guard (natp aval).

width — Guard (posp width).

Returns

ans — Type (bitp ans).

Definitions and Theorems

Function: vl-consteval-unary-reduxop

(defun vl-consteval-unary-reduxop (op aval width)
 (declare
  (xargs
   :guard
   (and (member op
                '(:vl-unary-bitand :vl-unary-nand :vl-unary-bitor
                                   :vl-unary-nor :vl-unary-xor
                                   :vl-unary-xnor :vl-unary-lognot))
        (natp aval)
        (posp width))))
 (let ((__function__ 'vl-consteval-unary-reduxop))
   (declare (ignorable __function__))
   (b* ((aval (lnfix aval))
        (width (lposfix width)))
     (case op
           (:vl-unary-bitand (if (equal (acl2::loghead width aval)
                                        (1- (expt 2 width)))
                                 1
                               0))
           (:vl-unary-nand (if (equal (acl2::loghead width aval)
                                      (1- (expt 2 width)))
                               0
                             1))
           (:vl-unary-bitor (if (posp aval) 1 0))
           (:vl-unary-nor (if (posp aval) 0 1))
           (:vl-unary-xor (if (oddp aval) 1 0))
           (:vl-unary-xnor (if (oddp aval) 0 1))
           (:vl-unary-lognot (if (posp aval) 0 1))
           (otherwise (progn$ (impossible) 0))))))

Theorem: bitp-of-vl-consteval-unary-reduxop

(defthm bitp-of-vl-consteval-unary-reduxop
  (b* ((ans (vl-consteval-unary-reduxop op aval width)))
    (bitp ans))
  :rule-classes :rewrite)

Theorem: vl-consteval-unary-reduxop-of-nfix-aval

(defthm vl-consteval-unary-reduxop-of-nfix-aval
  (equal (vl-consteval-unary-reduxop op (nfix aval)
                                     width)
         (vl-consteval-unary-reduxop op aval width)))

Theorem: vl-consteval-unary-reduxop-nat-equiv-congruence-on-aval

(defthm vl-consteval-unary-reduxop-nat-equiv-congruence-on-aval
  (implies (acl2::nat-equiv aval aval-equiv)
           (equal (vl-consteval-unary-reduxop op aval width)
                  (vl-consteval-unary-reduxop op aval-equiv width)))
  :rule-classes :congruence)

Theorem: vl-consteval-unary-reduxop-of-pos-fix-width

(defthm vl-consteval-unary-reduxop-of-pos-fix-width
  (equal (vl-consteval-unary-reduxop op aval (pos-fix width))
         (vl-consteval-unary-reduxop op aval width)))

Theorem: vl-consteval-unary-reduxop-pos-equiv-congruence-on-width

(defthm vl-consteval-unary-reduxop-pos-equiv-congruence-on-width
  (implies (acl2::pos-equiv width width-equiv)
           (equal (vl-consteval-unary-reduxop op aval width)
                  (vl-consteval-unary-reduxop op aval width-equiv)))
  :rule-classes :congruence)